Scala analysis: 14_13-parapyth17
Interpretation of Jake Freivald's Cantonpenta with just 14/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.786 cents 58.785690 2: 128.298 cents 128.298240 3: 208.085 cents 208.085210 4: 266.871 cents 266.870910 5: 346.658 cents 346.657870 6: 416.170 cents 416.170420 7: 474.956 cents 474.956120 8: 554.743 cents 554.743090 9: 624.256 cents 624.255630 10: 704.043 cents 704.042600 11: 762.828 cents 762.828300 12: 842.615 cents 842.615270 13: 912.128 cents 912.127820 14: 970.914 cents 970.913510 15: 1050.700 cents 1050.700480 16: 1120.213 cents 1120.213030 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 79.7870 cents 79.7870 1: 58.7857 cents 58.7857 2: 69.5125 cents 69.5125 3: 79.7870 cents 79.7870 4: 58.7857 cents 58.7857 5: 79.7870 cents 79.7870 6: 69.5125 cents 69.5125 7: 58.7857 cents 58.7857 8: 79.7870 cents 79.7870 9: 69.5125 cents 69.5125 10: 79.7870 cents 79.7870 11: 58.7857 cents 58.7857 12: 79.7870 cents 79.7870 13: 69.5126 cents 69.5126 14: 58.7857 cents 58.7857 15: 79.7870 cents 79.7870 16: 69.5126 cents 69.5126 17: 79.7870 cents 79.7870
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 58.78569 cents 1: 5 69.51255 cents 1: 7 79.78697 cents 2: 3 128.29824 cents 2: 7 138.57267 cents 2: 7 149.29952 cents 3: 13 208.08521 cents 3: 2 218.35963 cents 3: 2 229.08648 cents 4: 3 266.87091 cents 4: 3 277.59776 cents 4: 11 287.87218 cents 5: 8 346.65787 cents 5: 8 357.38473 cents 5: 1 367.65915 cents 6: 9 416.17042 cents 6: 4 426.44485 cents 6: 4 437.17169 cents 7: 1 474.95612 cents 7: 1 485.68297 cents 7: 15 495.95740 cents 8: 6 554.74309 cents 8: 6 565.46994 cents 8: 5 575.74436 cents 9: 5 624.25563 cents 9: 6 634.53006 cents 9: 6 645.25691 cents 10: 15 704.04260 cents 10: 1 714.31703 cents 10: 1 725.04388 cents 11: 4 762.82830 cents 11: 4 773.55516 cents 11: 9 783.82958 cents 12: 1 832.34085 cents 12: 8 842.61527 cents 12: 8 853.34213 cents 13: 11 912.12782 cents 13: 3 922.40224 cents 13: 3 933.12909 cents 14: 2 970.91351 cents 14: 2 981.64037 cents 14: 13 991.91479 cents 15: 7 1050.70048 cents 15: 7 1061.42734 cents 15: 3 1071.70176 cents 16: 7 1120.21303 cents 16: 5 1130.48745 cents 16: 5 1141.21431 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 58.8 128.3 208.1 266.9 346.7 416.2 475.0 554.7 624.3 704.0 762.8 842.6 912.1 970.9 1050.7 1120.2 1200.0 58.8 : 69.5 149.3 208.1 287.9 357.4 416.2 496.0 565.5 645.3 704.0 783.8 853.3 912.1 991.9 1061.4 1141.2 1200.0 128.3 : 79.8 138.6 218.4 287.9 346.7 426.4 496.0 575.7 634.5 714.3 783.8 842.6 922.4 991.9 1071.7 1130.5 1200.0 208.1 : 58.8 138.6 208.1 266.9 346.7 416.2 496.0 554.7 634.5 704.0 762.8 842.6 912.1 991.9 1050.7 1120.2 1200.0 266.9 : 79.8 149.3 208.1 287.9 357.4 437.2 496.0 575.7 645.3 704.0 783.8 853.3 933.1 991.9 1061.4 1141.2 1200.0 346.7 : 69.5 128.3 208.1 277.6 357.4 416.2 496.0 565.5 624.3 704.0 773.6 853.3 912.1 981.6 1061.4 1120.2 1200.0 416.2 : 58.8 138.6 208.1 287.9 346.7 426.4 496.0 554.7 634.5 704.0 783.8 842.6 912.1 991.9 1050.7 1130.5 1200.0 475.0 : 79.8 149.3 229.1 287.9 367.7 437.2 496.0 575.7 645.3 725.0 783.8 853.3 933.1 991.9 1071.7 1141.2 1200.0 554.7 : 69.5 149.3 208.1 287.9 357.4 416.2 496.0 565.5 645.3 704.0 773.6 853.3 912.1 991.9 1061.4 1120.2 1200.0 624.3 : 79.8 138.6 218.4 287.9 346.7 426.4 496.0 575.7 634.5 704.0 783.8 842.6 922.4 991.9 1050.7 1130.5 1200.0 704.0 : 58.8 138.6 208.1 266.9 346.7 416.2 496.0 554.7 624.3 704.0 762.8 842.6 912.1 970.9 1050.7 1120.2 1200.0 762.8 : 79.8 149.3 208.1 287.9 357.4 437.2 496.0 565.5 645.3 704.0 783.8 853.3 912.1 991.9 1061.4 1141.2 1200.0 842.6 : 69.5 128.3 208.1 277.6 357.4 416.2 485.7 565.5 624.3 704.0 773.6 832.3 912.1 981.6 1061.4 1120.2 1200.0 912.1 : 58.8 138.6 208.1 287.9 346.7 416.2 496.0 554.7 634.5 704.0 762.8 842.6 912.1 991.9 1050.7 1130.5 1200.0 970.9 : 79.8 149.3 229.1 287.9 357.4 437.2 496.0 575.7 645.3 704.0 783.8 853.3 933.1 991.9 1071.7 1141.2 1200.0 1050.7: 69.5 149.3 208.1 277.6 357.4 416.2 496.0 565.5 624.3 704.0 773.6 853.3 912.1 991.9 1061.4 1120.2 1200.0 1120.2: 79.8 138.6 208.1 287.9 346.7 426.4 496.0 554.7 634.5 704.0 783.8 842.6 922.4 991.9 1050.7 1130.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.7857 .. 79.7870 cents 21.00128 cents 58.78569 cents 2: 128.2982 .. 149.2995 cents 21.00128 cents 48.51127 cents 3: 208.0852 .. 229.0865 cents 21.00127 cents 58.78569 cents 4: 266.8709 .. 287.8722 cents 21.00127 cents 37.78443 cents 5: 346.6579 .. 367.6591 cents 21.00128 cents 58.78569 cents 6: 416.1704 .. 437.1717 cents 21.00127 cents 48.51127 cents 7: 474.9561 .. 495.9574 cents 21.00128 cents 37.78443 cents 8: 554.7431 .. 575.7444 cents 21.00127 cents 58.78569 cents 9: 624.2556 .. 645.2569 cents 21.00128 cents 48.51127 cents 10: 704.0426 .. 725.0439 cents 21.00128 cents 58.78569 cents 11: 762.8283 .. 783.8296 cents 21.00128 cents 37.78442 cents 12: 832.3409 .. 853.3421 cents 21.00128 cents 48.51127 cents 13: 912.1278 .. 933.1291 cents 21.00127 cents 58.78569 cents 14: 970.9135 .. 991.9148 cents 21.00128 cents 37.78442 cents 15: 1050.7005 .. 1071.7018 cents 21.00128 cents 58.78569 cents 16: 1120.2130 .. 1141.2143 cents 21.00128 cents 48.51127 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 58.78569 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 79.78697 cents Average / Smallest step : 1.200772 Largest / Average step : 1.130315 Largest / Smallest step : 1.357252 Median interval of one step : 69.51255 cents, amount: 5 Most common interval of one step : 79.78697 cents, amount: 7 Least squares average step : 69.85751 cents, oct.: 1187.57770 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCACBACBCACBACBC Step pattern size order : SMLSLMSLMLSLMSLML Scale is a Constant Structure, by a margin of 37.78442 cents Scale diversity : 1.195701 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.719983 Number of different interval sizes : 48 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 10.27442 cents Most common intervals : 495.95740 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 357.385 704.043 cents Most common triad is 0.0 495.957 704.043 cents, amount: 13 Number of recognisable fifths : 16, average 704.6848 cents Number of appreciable fifths : 15, average 704.0426 cents Best fifths form a closed circle Formal octave complements present : 1 = 5.8824% Limited transpositions with margin 21.0013 cents: 12 Limited inverse transpositions with margin 21.0013 cents: 2 7 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.6568 c. M:-19.1615 c. 30: 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 2 P D3 SD: 10.7514 c. M: 18.7857 c. 31: 2 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 P D3 S SD: 10.0334 c. M:-18.6337 c. 33: 2 2 2 1 3 1 2 2 2 2 2 2 2 2 2 2 2 P D3 S SD: 10.3624 c. M:-17.1563 c. 35: 2 2 2 2 2 2 2 2 2 3 1 3 2 1 3 2 2 P D3 SD: 9.3983 c. M:-15.9574 c. 37: 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 3 2 SP M ME S SD: 8.9348 c. M:-15.5501 c. 38: 2 2 3 1 3 2 2 3 2 2 2 3 2 2 2 2 3 P D3 SD: 8.5929 c. M: 14.9499 c. 41: 2 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 3 SP M ME S SD: 5.5032 c. M: 11.2251 c. 45: 2 3 3 2 3 3 2 3 2 3 3 3 2 2 3 3 3 SP D3 SD: 7.5483 c. M: 10.9223 c. 46: 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 3 SP M ME S SD: 4.9234 c. M: 7.8327 c. 58: 3 3 4 3 4 3 3 4 3 4 3 4 3 3 4 3 4 SP M ME S SD: 3.1405 c. M:-5.6606 c. 63: 3 4 4 3 4 4 3 4 4 4 3 4 4 3 4 4 4 SP M ME S SD: 2.7415 c. M:-5.0351 c. 104: 5 6 7 5 7 6 5 7 6 7 5 7 6 5 7 6 7 SP T3 SD: 1.0426 c. M: 1.8792 c. 121: 6 7 8 6 8 7 6 8 7 8 6 8 7 6 8 7 8 SP T3 SD: 0.6064 c. M:-1.0769 c. 225: 11 13 15 11 15 13 11 15 13 15 11 15 13 11 15 13 15 SP T3 SD: 0.1699 c. M: 0.2982 c. 346: 17 20 23 17 23 20 17 23 20 23 17 23 20 17 23 20 23 SP T3 SD: 0.1271 c. M:-0.1884 c. 571: 28 33 38 28 38 33 28 38 33 38 28 38 33 28 38 33 38 SP T3 SD: 0.0657 c. M:-0.1168 c. 1430: 70 83 95 70 95 83 70 95 83 95 70 95 83 70 95 83 95 SP T3 SD: 0.0560 c. M: 0.0978 c. 1551: 76 90 103 76 103 90 76 103 90 103 76 103 90 76 103 90 103 SP T3 SD: 0.0671 c. M:-0.1350 c. 1655: 81 96 110 81 110 96 81 110 96 110 81 110 96 81 110 96 110 SP T3 SD: 0.0443 c. M: 0.0775 c. 1776: 87 103 118 87 118 103 87 118 103 118 87 118 103 87 118 103 118 SP T3 SD: 0.0393 c. M:-0.0801 c. 1880: 92 109 125 92 125 109 92 125 109 125 92 125 109 92 125 109 125 SP T3 SD: 0.0453 c. M: 0.0625 c. 2001: 98 116 133 98 133 116 98 133 116 133 98 133 116 98 133 116 133 SP T3 SD: 0.0214 c. M:-0.0376 c. 2226: 109 129 148 109 148 129 109 148 129 148 109 148 129 109 148 129 148 SP T3 SD: 0.0187 c. M: 0.0277 c. 2347: 115 136 156 115 156 136 115 156 136 156 115 156 136 115 156 136 156 SP T3 SD: 0.0199 c. M:-0.0358 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.0438 cents 3 .. 6 match: 3 H SD: 12.0380 cents 4 .. 8 match: 4 H SD: 7.5006 cents 5 .. 10 match: 5 H SD: 12.1094 cents 6 .. 12 match: 6 H SD: 6.0332 cents 7 .. 14 match: 7 H SD: 6.7088 cents 8 .. 16 match: 8 H SD: 5.5257 cents 9 .. 18 match: 9 H SD: 6.2091 cents 10 .. 20 match: 10 H SD: 7.4643 cents 11 .. 22 match: 11 H SD: 4.9420 cents 12 .. 24 match: 12 H SD: 5.1855 cents 13 .. 26 match: 13 H SD: 4.0497 cents 14 .. 28 match: 14 H SD: 4.9104 cents 15 .. 30 match: 14 S SD: 6.3811 cents 16 .. 32 match: 15 SD: 4.0269 cents 17 .. 34 match: 14 S SD: 5.7491 cents 18 .. 36 match: 16 S SD: 4.3671 cents 19 .. 38 match: 16 SD: 4.5136 cents 20 .. 40 match: 16 SD: 5.2257 cents 21 .. 42 match: 17 SD: 4.7994 cents 22 .. 44 match: 17 SD: 3.4718 cents 23 .. 46 match: 17 SD: 3.0538 cents 26 .. 52 match: 17 SD: 2.8225 cents 29 .. 58 match: 17 SD: 2.5720 cents 30 .. 60 match: 17 SD: 2.5534 cents 32 .. 64 match: 17 SD: 2.1159 cents 37 .. 74 match: 17 SD: 2.0263 cents 40 .. 80 match: 17 SD: 1.8610 cents 48 .. 96 match: 17 SD: 1.4529 cents 53 .. 106 match: 17 SD: 1.3276 cents 54 .. 108 match: 17 SD: 1.2471 cents 64 .. 128 match: 17 SD: 1.1821 cents 67 .. 134 match: 17 SD: 1.1694 cents 76 .. 152 match: 17 SD: 1.0323 cents 77 .. 154 match: 17 SD: 0.9692 cents 78 .. 156 match: 17 SD: 0.8704 cents 85 .. 170 match: 17 SD: 0.7524 cents 92 .. 184 match: 17 SD: 0.7156 cents 108 .. 216 match: 17 SD: 0.6007 cents 117 .. 234 match: 17 SD: 0.5916 cents 132 .. 264 match: 17 SD: 0.5734 cents 140 .. 280 match: 17 SD: 0.4838 cents 143 .. 286 match: 17 SD: 0.4335 cents 170 .. 340 match: 17 SD: 0.4304 cents 180 .. 360 match: 17 SD: 0.3068 cents 235 .. 470 match: 17 SD: 0.1905 cents 352 .. 704 match: 17 SD: 0.1759 cents 376 .. 752 match: 17 SD: 0.1712 cents 408 .. 816 match: 17 SD: 0.1688 cents 415 .. 830 match: 17 SD: 0.1506 cents 431 .. 862 match: 17 SD: 0.1438 cents 456 .. 912 match: 17 SD: 0.1287 cents 522 .. 1044 match: 17 SD: 0.1209 cents 558 .. 1116 match: 17 SD: 0.1186 cents 574 .. 1148 match: 17 SD: 0.1115 cents